Continuous Subarray Sum - Leetcode 523 - Python

[@mdazharuddin4684]

We add {0 : -1} in dict not to handle case where 1st element is divisible by k. We add it to handle case where subarray starting from 0 is divisible by k. For example when k = 6 and nums = [1,2,3,4] and we don't initialize 0, we will get False.

[@xinl9259]

Thanks! I watched the video and could not understand why {0:-1} and you answered my question. Very appreciate!

[@shin-wu]

Great addition to the video! Thanks for the clarification.

[@halahmilksheikh]

Yep. Also a way to get rid of that is to have `if (remainder == 0 && i > 0) return true` in the for loop

[@a_maxed_out_handle_of_30_chars]

yeah, this makes sense

[@AbhishekMakwana-p1v]

you Can Just Add this Condition if sum%k==0 and i>=1: return True

[@khanofkhans4832]

Continuous Subarray Sum of PAIN

[@Ginger_Hrn]

in the arse

[@ObtecularPk]

Again, how is someone able to come up with a solution like this in a time limit interview? This is the question that needs answering next video or something

[@easynow6599]

i am thinking the same..in most of these problems..I guess there are three ways: a) you should know the problem beforehand and solve it..so it would be relatively easy to repeat during interview..b) you get plenty of help from the interviewer and you kinda solve it with bugs or/and pseudocode..c) you have spend your life with LC and you solve it in 15' seeing first time.. I dont see myself even close to option c and i guess i have to practice 10 times more..but i would be curious if someone who has passed the interview can tell

[@halahmilksheikh]

Step 1: Solve it before the interview Step 2: Solve it during the interview and pretend you've never seen it

[@rams2478]

I second that... looks interview is pure luck...

[@josecabrera7947]

@@easynow6599 I had an interview with a big tech company like last week. I was able to solve roughly 2 problems that I had never seen before that I would categorize as leetcode easy's. They had edge cases that took time and killed like 35 min. The other two however one was hard and the other was either hard or medium. I had no idea how to solve them. I was able to get some work in but couldnt pass all the cases. I later looked them up for hours and was able to find 1 similar but not entirely the same. I spent like 2 hours trying to understand and solve the problem I found. There is no way someone can solve these in 15 minutes.

[@easynow6599]

@@josecabrera7947 i dont know man..this leetcode looks like a BS system.. but discussing about that i think it's the optimal way to filter people..with a lot of false negatives (a lot of good people stay out because a problem was too hard to solve) and a some false positives (people that grind LC as hell, but in reality they dont know much stuff).. Anyway..i wish you good luck!

[@dantesmith7859]

I wrestled with this one for a couple hours... I was trying to store the prefix sum, not the remainder, and I was having a tough time making that work. Storing the remainders is a great idea, and made the code much more concise! Thanks!

[@kuancs1]

Dude if I was in your shoes and realised that I was effectively ramming my head in a wall for a few hours, I would definitely not have the calmness of mind you do. Admire the positivity.

[@mirceskiandrej]

This is not a medium question. It is hard, borderline extreme. If you see the solution, it becomes easy since it's memorable, but you cannot average easy and hard to get a medium question 😃

[@shanemarchan658]

ikr. for days ive been trying LOL... really out of the box thinking to come up with this

[@shivamshah6579]

100% true!

[@CS_n00b]

I was asked this question for a new grad job at a small company fml

[@avanishgvyas1992]

Nice explanation. Impossible to come up with this solution in 25 minutes while under stress in an interview.

[@redblacktech]

awesome vid! i'd like to add that the optimized solution is like two-sum in the sense that we're caching complementary values. once you see it this way it becomes intuitive, however, there's no way in hell the average person is going to figure that out without tons of practice doing leetcode questions specifically 🙃 i'd ALSO like to add a one line intuition for the key point of this video: if we see two numbers that when % by k have the same remainder, then those numbers are either k away from each other (or multiple of k away from each other) - and this is exactly what the problem is asking us to find

[@finchshi4342]

bro you are my favorite leetcode channel

[@NeetCode]

Appreciate that :)

[@erikshure360]

yeah, fuck this problem.

[@hanklin4633]

Is it possible to think of hashing the remainder in an actual interview? What 'intuition' could anyone even come up with it in the first place?

[@adam-zy5tb]

wouldn't space complexity be O(k) since you are storing at most k entries in the hashmap? i.e. if k = 6 you are storing at most 6 entries since the remainder would never be more than 5 (+1 more for the 0 edge case)

[@ivankok8399]

Nice solution and explanation. I was struggling to find a faster solution, but this duplicate remainder approach is very creative!

[@AlexN2022]

the easier-to-come-up-with solution can still work: 1. calculate prefix array and store in a map (sum->leftmost index where found) 2. r = 0; r < size; r++ 3. calculate the current rmdr = sum%k 4. if we could find a sub-array on the left with sum=rmdr, we could remove that subarray from [0:r] and sum%k would be 0 5. look for rmdr in the map. If found && index < r - we have found the sub-array to remove

[@metarun]

dude.. your setup to explain these problems is very efficient. Thanks for putting in the hardwork. cheers

[@Dumbastic]

Thank you for the clear explanation, I saw the solution before, but I couldn't get behind why it was neccessary to have a duplicated modulo result value in the array. You were able to explain it in a simple manner, appreciate it a lot! Keep up the good work! :)

[@CreeperFace75]

great vid! No idea how u come out with these solutions but they make perfect sense

[@vadimkokielov2173]

first i want to make sure you, but also anyone else knows. I am not writing suggestions because I don't need your videos and the help they give. I need them a lot. I am intensively preparing for an interview. Whatever I write is anything I discover on top of your solutions. That said...You can spare the map and use a hash set. Just keep it trailing behind by one index, so you don't get any invalid values. I am sure you know this solution, and if you decided not to explain it because the mind xxxx of the problem itself is pain enough, then I absolutely agree with you. It's worth pointing out, however.

[@hershjoshi3549]

yeah you can def do it with a set and a prev value where prev = sum % k. Personally I find the hashmap solution a little easier to understand and remember.

[@priyankachoudhary3694]

Amazing explanation! I don't think I would have been ever able to understand this question without your elegant and detailed explanation about what works and what doesn't work and why it doesn't work.

[@varunshrivastava2706]

I was asked the same question in my Accolite Digital interview, glad I had already solved it before otherwise I would have been doomed!!!!

[@Ryan-g7h]

Hey guys also don't forget this video is missing a key detail: look into why we use elif i - remainder[r] > 1 instead of >=. It ties to the {0:-1} and a edge case such as [6,1,2], k = 6 -> should false but if we do >= return True

[@rongrongmiao3018]

I hate math questions. To solve this problem all we need to know is that (a-b)%c = ((a%c) - (b%c)) % c. so to get a-b mod c = 0, just need to have this: a mod c = b mod c

[@vdyb745]

Awesome explanation.... for an insane problem. Great work !!!!!

[@algosavage7057]

just best. I'm watching you for about a year and just wanna say that u'r the best! Thanks for ur job!

[@tusharnain6652]

Only explanation that my brain understood. Thank you Neetcode.

[@poptart007-b2r]

Omg the the solution is so damn cool ! I tried out the same lines you talked about in the beginning but it led me nowhere so i was feeling pretty dumdum :p Thank you for your clear explanation as always, it really helps :)

[@shadowthehedgehog2727]

Damn this solution is crazy.. i don’t think I would even think of this

[@danielcontreras9343]

I am a continuous sub array

[@sitam-meur4317]

This solution is just awesome !!! Thanks @NeetCode .

[@SomneelMaity]

Amazing Explanation Bro. Your explanation videos made my DSA skills far better.

[@shelbys4252]

only leetcoder who makes sense tbh. Well done.

[@jitpatel1105]

Nice Explanation,Thank You

[@samridhanand4926]

The thought process that helped me get to the solution was by thinking of the problem Largest Subarray with sum 0, as we use hashmap to store the sum with index.

[@chandamwenechanya8614]

Hey neet, this is neat!

[@henryrussell7392]

Amazing explanation as always

[@anirbannandy9104]

Definitely Like Your Work Bro......Your Explanation Rocks!!!!

[@andrewpagan]

Thank you so so so so soooo much for this. I was on the right track with modulo and thinking of a sliding window, but was missing the last piece with prefix sum.

[@mrunalajitjoshi1512]

You got a new subscriber!!

[@aadityakiran_s]

Got asked a harder variation of this in a Google interview. No real hint was also provided by the interviewer. I suppose luck is also a factor. If you've seen the problem before or if you're able to fit whatever problem, you get into the pattern that you've seen before.

[@meetsoni1938]

You made it very easy for me 🔥🔥💯

[@clumsyroad4026]

Your original trains of thought about the 2sum problem as well as a prefix sum approach were also doable, if you had dived deeper into them and made minor modifications. Here is a 2sum-like approach to solving this problem in one pass: class Solution: def checkSubarraySum(self, nums: List[int], k: int) -> bool: seen = set() prv = cur = 0 for x in nums: cur, prv = (cur + x) % k, cur if cur in seen: return True seen.add(prv) return False

[@ayushidalal5488]

Hey, I'm new to this channel. I loved how you explained it so easily! Thanks :)

[@bluesteel1]

I feel you need to be good at math to crack this one on your own.

[@beinghappy9223]

Amazing intuition

[@ShivangiSingh-wc3gk]

Yeah, after coming to prefix sums, I couldnt think about this so tricky either you see the math or you dont

[@venkatasundararaman]

I have been watching your videos and May be it helped I don’t know but I had the same idea to solve the problem before seeing the solution 😃

[@rishabhraj8233]

great explanation bro💗

[@vinuk.vijayakumar8023]

used this to solve 974. made a few changes. def checksumarray_k(nums, k): remainder={0:[-1]} total=0 count=0 for idx, element in enumerate(nums): total+=element r=total%k if r not in remainder: remainder[r]=[idx] else: count+=len(remainder[r]) remainder[r].append(idx) return count

[@mojedsamad7184]

What if we wanted to know where or wich list entries give us this multiple?

[@shikharathaur5179]

Very well explained !

[@MrAdnan252]

Is the two consecutive 0's not a valid input? You mentioned it, and as you said it wouldnt change the remainder from 23, so how do you detect it as a solution?

[@sidazhong2019]

2 sum or sliding windows. Your false ideas were exactly what I was trying to do.

[@fazilshafi8083]

Java Solution: class Solution { public boolean checkSubarraySum(int[] nums, int k) { HashMap map = new HashMap(); // To store int prefixSum = 0; map.put(0, -1); for (int i = 0; i < nums.length; i++) { prefixSum += nums[i]; int remainder = k == 0 ? prefixSum : prefixSum % k; if (map.containsKey(remainder)) { int length = i - map.get(remainder); if (length >= 2) { return true; } } else { map.put(remainder, i); } } return false; } }

[@IK-xk7ex]

Yep, it's hard to come up with the part 'i-remainder[r] > 1' by my own. It's great that we leave in the era of streaming to gain best practices

[@unknown_manushya]

I managed to do this on my own with prefix sum approach. My approach is different though and is more than O(n). Following is the code. bool checkSubarraySum(vector& nums, int k) { int sum = 0; unordered_map hash; for (int i = 0; i < nums.size(); i++) { sum += nums[i]; if (!i) { hash[sum] = i; continue; } if (sum % k == 0) return true; int j = 0; while (k * j < sum) { int rem = sum - k * j; if (hash.count(rem) && i - hash[rem] >= 2) { return true; } j++; } if (!hash.count(sum)) hash[sum] = i; } return false; }

[@vedbhanushali608]

thanks, great intution.

[@lesterdelacruz5088]

Mind blown. Who would've come up with that trick from the get go haha?

[@mohammadkareem1187]

Very elegant explanation. Thanks a lot. Can you please do Leetcode 2060 as well?

[@mariotheguy123]

thank you neet

[@mohamed_ellithy]

AMAZING IDEA 😍🌹

[@kaushik.aryan04]

I think because of this approach this should have been marked as hard problem.

[@tomtran6936]

There is a step after calculating r you can also check if r == 0 return True

[@Will-dr9cf]

The time complexity of the brute force solution (by summing up the sub-arrays in sliding windows with cumulative sum) seems to be O(n!), which is worse than O(n^2).

[@mattjm007]

Well done on this video

[@srinivasareddychalla-i2o]

So key point here is if prefixsum%k=r and (prefixsum+x1+x2+•••••+xn)%k=r then undoubtedly x1+x2+•••••+xn is multiple of k

[@irarose3536]

Thanks!

[@abhishekgururani6993]

Another way to handle the edge case when prefix sum will itself be a multiple of k, arr = [24,0,2] k = 6, [24,0] subarray sum is a multiple of 6. if(prefSum % k == 0 && idx > 0) return true;

[@vinayakhaunsnur1327]

great solution

[@DJSTEVE42]

Does any one know why when we encounter a remainder that already exists in the hash map, there exists a sum that is %k ?

[@dragonoid296]

because if the remainder wraps around, we know that it changed by k

[@Everafterbreak_]

If you get this in an interview and you haven't seen this before you're definitely cooked, theres no way any person will come out with this intuition.

[@rajeevkri123]

Java solution for the same public boolean checkSubarraySum(int[] nums, int k) { HashMap map = new HashMap (); int sum = 0; map.put(0, -1); boolean found = false; int n = nums.length; for(int i=0; i< n; i++) { sum = sum + nums[i]; int hash = sum % k; if(map.containsKey(hash)) { int diff = i - map.get(hash); if(diff>=2) { found = true; break; } } else { map.put(hash, i); } } return found; }

[@bokistotel]

I think this is not about having a math brain, it is about have you seen enough of these similar patterns from the past so your brain gets used to it.

[@ujjaldas9179]

thanks

[@ratnadeeppaul]

what happens if r is already in the hashmap but index difference is less than 1?

[@edwardteach2]

U a Continuous Subarray Sum God

[@yashpathak9285]

You are so smart!! I would like to elect you president.

[@madhuj6912]

Can someone tell me whats this , what is x and n are that values of array " An integer x is a multiple of k if there exists an integer n such that x = n * k. 0 is always a multiple of k "

[@codeguru4]

hi @neetcode i Try to solve it Using Sliding Window It passes Most of the Test Csaes but if array consist of 0 then its failing 93/99 test cases are passed but this one if failing nums = [1,3,6,0,9,6,9]. , k = 7 output : True if len(nums) < 2: return False currSum = 0 totalSum =nums[0] l= 0 for r in range(1, len(nums)): currSum = nums[l]+ nums[r] totalSum +=nums[r] if currSum % k == 0 or totalSum % k == 0 : return True l+=1 if totalSum % k == 0: return True return False could you please See It Please

[@bhushanmahajan2150]

Could you please make videos on systems designs as well, if possible?

[@ariaXP1]

Can you do 410. Split Array Largest Sum? Thank you!!

[@SaahasBuricha]

this is insane

[@avanishraj386]

Could it be solved using Brute force method? If solved, then how?

[@zz-yy-xx]

OMG, so tricky!!!!!

[@kaioken1999]

Dope

[@santoshr4212]

this should have been a hard problem.

[@experiment0003]

Python is so easy for OA. Sadly, I'm more comfortable writing in Java. Imagine "remainder = { 0, -1 }". Java would be first import Map and hashMap, then Map remainder = new HashMap(); map.put(0, -1);. So sad. So so sad!

[@masternobody1896]

me as a day of life an unemployed dude :(

[@MDEMANURRAHAMAN-]

[5,0,0,0] 3 Expected output : True How can it possible ??

[@jsalaat]

0 and 0 are a continuous subarray hence making 0+0 = 0%k expects to fulfil the condition. hence returns true

[@vbcarnage]

i did not try it but it looks like this could be solved with segment trees

[@heetshah7292]

I was recently asked this question in an interview and I was solving it through a two-pointer approach but I failed to optimize and got rejected 😥

[@sureshsingam7291]

which company??

[@maheshj01]

This problem is mainly optimization.

[@Dannnneh]

Is there a real life use case for an algorithm for this?

[@sabukuna]

doubt it

[@RiazKhan-b6e]

How can a person reached this solution without exploring discussion or solution section?

[@rahulbhardwaj4380]

Great concept but really this approach is difficult to come up with.

[@gabrielignat4371]

that should be a HARD question

[@imjusttryingtobesafelol5909]

i laughed when i saw the solution its sooooooo clever

[@charanpasupula3763]

Ninja level

[@youssefel-shabasy833]

oh god

[@mayanksood4709]

Bro this is impossible for me to come up with!

[@yatri6329]

Great yaar i was missing some cases ... thanks

[@PREETIGUPTA-l8j]

Still unable to understand how it has checked all subarrays' sum

[@eddiej204]

How much IQ is required here to come up with the solution on the first look?

[@Ginger_Hrn]

idk, last time I solved a matrix problem to which the algorithm was made by a russian computer scientist to solve THAT particular type of problem.